Raskolnikov is right: you can't prove a definition. You can prove, however, that this is a good definition, i.e. that the limit exists, and is finite.

So, I'm trying to find as many definitions of $e$ in order to see just how many of these identities can actually be a definition of $e$. So far, I've got the following (which are the ones most …

Feb 8, 2018 · Proof of e as a limit Ask Question Asked 7 years, 10 months ago Modified 7 years, 10 months ago

Jul 15, 2016 · The limit definition of $e$ gives the best intuition toward how $e$ can model continuous growth. $$\lim\limits_ {n \to \infty} \left ( 1 + \frac1n\right)^n$$ Let n represent n …

Aug 20, 2017 · Is there a way to prove that the derivative of $e^x$ is $e^x$ without using chain rule? If so, what is it? Thanks.

Are you familiar with Taylor series? Series solutions of differential equations at regular points? From what foundation/background are you approaching this problem?

Apr 12, 2013 · Now $e (0)=e' (0)=1$ implies that the tangent line to $e (t)$ at $0$ is $t \mapsto 1+t$, and so for sufficiently small $t$ we should have $e (t)\simeq 1+t$, which this …

Jul 19, 2016 · I want to understand something about the derivation of $\\text{Var}(X) = E[X^2] - (E[X])^2$ Variance is defined as the expected squared difference between a random variable …

Oct 28, 2014 · e as sum of an infinite series [duplicate] Ask Question Asked 11 years, 1 month ago Modified 10 years, 11 months ago

Feb 15, 2018 · There are three ways to interpret this question. You could be asking "what is the difference between the two directions of implication?". You could be asking "what, intuitively, is …